Hopf bifurcation and uncontrolled stochastic traffic-induced chaos in an RED-AQM congestion control system

被引：7

作者：

Wang Jun-Song ^{[1
]}

Yuan Rui-Xi ^{[2
]}

Gao Zhi-Wei ^{[3
]}

Wang De-Jin ^{[4
]}

机构：

[1] Tianjin Med Univ, Sch Biomed Engn, Tianjin 300070, Peoples R China

[2] Tsinghua Univ, Sch Informat Sci, Beijing 100084, Peoples R China

[3] Tianjin Univ, Dept Automat, Tianjin 300072, Peoples R China

[4] Tianjin Univ Sci & Technol, Dept Automat, Tianjin 300222, Peoples R China

来源：

CHINESE PHYSICS B | 2011年 / 20卷 / 09期

基金：

国家高技术研究发展计划(863计划);

关键词：

stability; Hopf bifurcation; chaos; stochastic traffic; FLUID-FLOW MODEL; COMMUNICATION DELAY; CONTROL ALGORITHM; RECURRENCE PLOTS; STABILITY; INTERNET; NETWORKS; DESIGN; TCP;

D O I：

10.1088/1674-1056/20/9/090506

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study the Hopf bifurcation and the chaos phenomena in a random early detection-based active queue management (RED-AQM) congestion control system with a communication delay. We prove that there is a critical value of the communication delay for the stability of the RED-AQM control system. Furthermore, we show that the system will lose its stability and Hopf bifurcations will occur when the delay exceeds the critical value. When the delay is close to its critical value, we demonstrate that typical chaos patterns may be induced by the uncontrolled stochastic traffic in the RED-AQM control system even if the system is still stable, which reveals a new route to the chaos besides the bifurcation in the network congestion control system. Numerical simulations are given to illustrate the theoretical results.

引用

页数：6

共 24 条

[1] DISCRETE DELAY, DISTRIBUTED DELAY AND STABILITY SWITCHES [J].

COOKE, KL ;

GROSSMAN, Z .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1982, 86 (02) :592-627

[2] Delay induced Hopf bifurcation in a dual model of Internet congestion control algorithm [J].

Ding, Dawei ;

Zhu, Jie ;

Luo, Xiaoshu ;

Liu, Yuliang .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2009, 10 (05) :2873-2883

[3] Hopf bifurcation analysis in a fluid flow model of Internet congestion control algorithm [J].

Ding, Dawei ;

Zhu, Jie ;

Luo, Xiaoshu .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2009, 10 (02) :824-839

[4] RECURRENCE PLOTS OF DYNAMIC-SYSTEMS [J].

ECKMANN, JP ;

KAMPHORST, SO ;

RUELLE, D .

EUROPHYSICS LETTERS, 1987, 4 (09) :973-977

[5] Necessary and sufficient conditions for Hopf bifurcation in exponential RED algorithm with communication delay [J].

Guo, Songtao ;

Liao, Xiaofeng ;

Liu, Qun ;

Li, Chuandong .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2008, 9 (04) :1768-1793

[6] Stability and Hopf bifurcation analysis in a novel congestion control model with communication delay [J].

Guo, Songtao ;

Liao, Xiaofeng ;

Li, Chuandong .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2008, 9 (04) :1292-1309

[7] Linear stability and Hopf bifurcation analysis for exponential RED algorithm with heterogeneous delays [J].

Guo, Songtao ;

Liao, Xiaofeng ;

Liu, Qun ;

Wu, Haixia .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2009, 10 (04) :2225-2245

[8]

Hale J.K., 1977, THEORY FUNCTIONAL DI

[9] Analysis and design of controllers for AQM routers supporting TCP flows [J].

Hollot, CV ;

Misra, V ;

Towsley, D ;

Gong, WB .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2002, 47 (06) :945-959

[10] Design of adaptive PI rate controller for best-effort traffic in the Internet based on phase margin [J].

Hong, Yang ;

Yang, Oliver W. W. .

IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, 2007, 18 (04) :550-561

← 1 2 3 →